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2 years ago

9

Distance that sound travels through air d varies directly as time t, and d=1,675 ft when t=5 seconds, find t when d=5025ft

1 answer:

Marysya12 [62]2 years ago

5 0

Divide 5025 by 1675 then whatever you get multiply it by 5 that will get you t when d is 5025

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Rewrite square root of -49-4

Nataliya [291]

Answer:

$\sqrt{53i}$

Step-by-step explanation:

We need to find $\sqrt{-49-4}$

We know that √-1 = i

Adding -49 and -4 and solving

$\sqrt{-49-4}\\\sqrt{-53}\\\sqrt{53i}$

Since 53 is not a perfect square so our answer is:

$\sqrt{53i}$

7 0

2 years ago

Part A: Find a rational number that is between 7.7 and 7.9. Explain why it is rational. (2 points)

8_murik_8 [283]

A rational number is any number that can be written as the ratio between two other numbers i.e. in the form $\frac{a}{b}$

Part A:
An easy choice that makes sense is 7.8, right in the middle. To prove that it's rational we need to write it as a ratio. In this case we have $7.8=\frac{78}{10}$

Part B:
We need a number that can't be written as a ratio (because it neither terminates nor repeats). Some common ones are $\sqrt{2}$ , $e$ , $\phi$ and $\pi$ so it makes sense to try and use those to build our number. In this case $\frac{11\sqrt{2}}{5}\approx7.78$ works nicely.

6 0

3 years ago

You are given the parametric equations x=2cos(θ),y=sin(2θ). (a) List all of the points (x,y) where the tangent line is horizonta

vladimir1956 [14]

Answer:

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

Step-by-step explanation:

The slope of the tangent line at a point of the curve is:

$m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

$m = -\frac{\cos 2\theta}{\sin \theta}$

The tangent line is horizontal when $m = 0$ . Then:

$\cos 2\theta = 0$

$2\theta = \cos^{-1}0$

$\theta = \frac{1}{2}\cdot \cos^{-1} 0$

$\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)$ , for all $i \in \mathbb{N}_{O}$

$\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}$ , for all $i \in \mathbb{N}_{O}$

The first four solutions are:

x: $\sqrt{2}$ $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$

y: 1 -1 1 -1

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

6 0

2 years ago

What is the quotient of 3,968 ÷ 32

Arisa [49]

Answer:

124

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Solve the equation. \dfrac18 + c = \dfrac45 8 1 +c= 5 4 start fraction, 1, divided by, 8, end fraction, plus, c, equals, sta

aivan3 [116]

Answer:

$c=\dfrac{27}{40}\\$

Step-by-step explanation:

We are required to solve for c in the equation: $\dfrac{1}{8}+c= \dfrac{4}{5}$

Step 1: Collect like terms

$\dfrac{1}{8}+c= \dfrac{4}{5}\\c= \dfrac{4}{5}-\dfrac{1}{8}$

Step 2: Find the Lowest Common Multiple of the denominators

LCM of 8 and 5 is 40

Step 3: Multiply all through by 40

$40c= \dfrac{4}{5}*40-\dfrac{1}{8}*40$

Step 4: Simplify

40c=32-5

40c=27

Step 5: Divide both sides by 40 and simplify if possible.

$c=\dfrac{27}{40}\\$

4 0

3 years ago